The composition

$$\lambda_{H}=\pi_{\mathcal{F}}\circ\operatorname{Log}:H^{\circ}\to\Sigma_{n}$$

is a stratified $T^{n}$-fibration in the sense of Definition 7. It satisfies to all conclusions of Theorem 3 except for the third one. The fibration $\lambda_{H}$ can be deformed so that the third condition will also hold.